Question

The Dow Jones Industrial Average measures the performance of 30 large, publicly traded U.S. companies. An economist claims to have devised a theory that allows him to predict in advance whether the final (hundredths-place) digit of the Dow will be odd or even at the close of trading on Friday. He agrees to allow you to evaluate his predictionability. For fifty Mondays, he will tell you his prediction of the last digit of the Dow on the coming Friday. You will test the null hypothesis that his predictions are no more accurate than chance against the suitable one-sided alternative.

a. Suppose that over the 50 weeks of your evaluation, the economist makes 34 correct predictions. What is the result of the hypothesis test?

b. What conclusion should you draw from the test?

Answer 1

Answer:

Given that:

The Dow Jones Industrial Average measures the performance of 30 large, publicly traded U.S. companies.

a)  Suppose that over the 50 weeks of your evaluation, the economist makes 34 correct predictions. What is the result of the hypothesis test?

Ho: p=0.5


H:p > 0.5
(Right tail test)

Level of Significance, α = 0.05
Number of Items of Interest, x = 34
Sample Size, n = 50

Sample Proportion :

p=r/n

P=0.6800

Standard Error

SE = (1-P)/n)

SE = 0,0707

Z Test Statistic

P-p SE

(0.6800 - 0.5) 0.0707

0.18 0,0707

= 2.5456

p-Value = 0.0055 [Excel function =NORMSDIST(-z) ]

Decision: p-value<α , reject null hypothesis

b) What conclusion should you draw from the test?

There is enough evidence to conclude that his predictions are more accurate than chance.